Groepswerk

wiskunde

Groupwork

Mathematics

Eva Piessens en Samia Van den Bosch

4MTWIb nrs.1 en 4

__Lambert
Adolphe Jacques Quetelet__

Born: 22 february 1796 in Ghent, Belgium

Died: 17 february 1874 in Brussels, Belgium

**---/---------/---------/---------/---------/---------/---------/---------/---------/->**

1819… 1823… 1833… 1869… 1874… 1819… 1828… 1835… 1853

1819: he received his first doctorate on the theory of conic sections

1823: he went to Paris to study astronomy

1828: he founded the Royal Observatory at Brussels

1833: he worked on statistical, geophysical and meteorological data

1835: he wrote ‘sur l’homme et le développement de ses facultés, essai d’une physique sociale.’

1853: he organised the first international statistics conference

1869: his book was republished

__Quetelet's
biography__.

* Quetelet was born in Ghent on February the 22th. Right before his birth, on October the first, the Belgian provinces which had been submitted to the authorities of Austria since 1713, were now joined to the French Republic and that didn’t change until 1814.The years of education of Quetelet harmonize with the period of the French influence and in his work we can find the reflection of this influence.

* Quetelet lost his father at the age of 7 years. That is why he was forced to earn his money by himself. After his secondary studies he took a job as a professor of maths in Ghent. At that time, Quetelet came in touch with arts like painting, music and literature. This also explains his interest for the measures of taille and weight of men and also for the literary production.

* In 1819 Quetelet received his first doctorate in Ghent for a dissertation on the theory of conic sections. After having received this doctorate, he taught mathematics in Brussels.

* Then, in 1823; he went to Paris to study astronomy at the observatory there. He learnt astronomy from Araga an Bouvard, and the theory of probability under Joseph Fourier and Pierre Laplace.Influenced by Laplace and Fourier, Quetelet was the first to use the normal curve other than as an error law. His studies of the numerical consistency of crimes stimulated wide discussions of free will versus social determinism.

* Then he lectured at the Brussels atheneum, military college and museum.

* In 1828 he founded and directed the Royal Academy.

* For the Dutch, and later the Belgian government he collected and analysed statistics on crime, mortality and other subjects and devised improvements in census taking. His work produced great controversy among social scientists of the 19th century.

* The first publications of Quetelets social sciences were published in 1831. Quetelet also developed methods for simultaneous observations of astronomical, meteorological, and geophysical phenomena from scattered points throughout Europe.

* At an observatory in Brussels which he had established in 1833 at the request of the Belgian government, he worked on statistical, geophysical and meteorological data and he studied meteor showers. Quetelet established methods for the comparison and evaluation of the data.

* Under the influence of Garnier, professor of maths, at the university of Ghent, Quetelet decided to occupy himself with mathematics from now on.

* When Quetelet was 35 years old, he discovered a new curve. Immediately he was called to Brussels to occupy himself with the study of the elementary mathematics of Athene.

* A few months later, he was elected to be a
member of the Royal Academy of Science and Literature of
Brussels. When Quetelet arrived in Brussels, his activities
followed each other at a higher speed. He founded the
"Correspondance mathématique et physique", and
directed it together with Garnier from 1825 till 1827, and then
continued alone until 1839. In "Sur l’homme et le
développement de ses facultés, essai d’une physique
sociale."(1835) Quetelet presented his conception of the
average man as the central value about which measurements of a
human trait are grouped according to the normal curve. This book
was republished in 1869 as "Physique sociale.". The
internationally used measure of obesity is the *Quetelet index*.
This is:

QI = (weight in kilograms)/(height in metres)^{2}

If QI > 30,then a person is officially obese.

* Also nice to know: there is a Crater Quetelet on the moon!

* To end with, we can say that Quetelet played a very importante role in the international scene. He coordinated the collection and the treatment of the statistical data.

__Charles
Jean Gustave Nicolas de la Vallée Poussin__

Born : 14 August 1866 in Louvain, Belgium

Died : 2 March 1962 in Louvain, Belgium

**---/---------/---------/---------/---------/---------/---------/->**

1890… 1893… 1896… 1908… 1914 to 1918… 1928

1890 : he received his engineering diploma

1893 : after Gilbert, he got the chair for pure maths at the university of Louvain

1896 : he proved the prime number theorem

1908 : he was elected to be a member of the Royal Academy

1914 until 1918 : he taught in Paris where he met Henri Lebesgue

1928 : he received the titel of baron

__VALLEE
POUSSIN'S Biography__

* De la Vallée Poussin was born in Louvain August 14, 1866

* His father was a Frenchman and professor of geology at the University of Louvain . His mother belonged to the Belgian nobility.

* At first Vallée Poussin thought he would become a Jesuit. He entered the Jesuit college at Mons but he found the teaching there unacceptable and left.

* After this he turned to engineering and obtained his diploma in that subject. (1890)

- Influenced by Louis Gilbert, he became attracted to pure mathematics.In 1891 Vallée Poussin was made an assistant at the University of Louvain. He worked with Gilbert, who had been one of his teachers. But after the death of Gilbert,Vallée Poussin was elected to Gilbert’s chair in 1893. He was 26 years old by then.
- In 1896 he was the first to prove ’the prime number theorem’giving a correct answer to the question : "How many primes are there less than or equal to x ?"(for x any natural number greater than 1)
- * In 1908 he’s elected to be a member of the Royal Academy.

* During the First World War, Vallée Poussin leaves Louvain and goes to Paris where he was a teacher at ‘collège de France’. This is also the school where he met Henri Lebesgue (1875-1941)

* Vallée Poussin‘s most major work was ‘Cours d’analyse’. It went through several editions, each containing new material. The third edition of Volume 2 was burned by the German army when it overran Louvain. It would have discussed the Lebesgue integral, work which was never meant to be published. Unlike many similar books of its time ‘ Cours d’analyse’ contains no complex function theory.

* After 1925 Vallée Poussin turned to complex variable, potential theory and conformal representation. However publication of his work ‘Le potential logarithmique’ was held up by the war and only published in 1949

* On May 13, 1928 he received the titel of baron.

*When he’s 85 years old, he stopped teaching.

* He dies on March 2, 1962 in Watermaal-Bosvoorde. He was 96 years old.

**The Prime Number Theorem :
approximating pi(x)**

Over 2000 years ago Euclid proved that the number of primes is infinite and at first sight the primes seem to be distributed among the naturals in rather a haphazard way. For example between 1 and 100 we find 25 primes and in the 100 numbers immediately before 10 000 000 there are 9 primes, while in the 100 numbers after there are only 2 primes. However, on a large scale, the way in which the primes are distributed is very regular.

….. 0 ..100 . 200 . 300 . 400 . 500 . 600 . 700 . 800 . 900. 1000

Legendre and Gauss both did extensive calculations of the density of primes.

In 1798 Legendre gave as estimate for pi(x) : x / (ln x - 1.08366)

Gauss wrote at the back of his notebook : Primzahlen unter x (=¥ ) : x / ln x

We are not sure whether Gauss proved this statement.

Finally in 1896 de la Vallée Poussin and also, in the same year independently and in a different way, the French mathematician Hademard completely proved the prime theorem.

The assumption made by Gauss was correct :

"The larger x the better pi(x) approaches x / ln x and the difference between pi(x) and this estimation can be made as small as you want if x is taken large enough" |

__Here we found our information__**:**

*** **For the pictures : word-insert-picture**
**

*** **Encyclopaedia Brittannica

* Internet

- http://www-history.mcs.st-and.ac.uk/history/HistTopics/Prime_numbers.html
- http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Vallee_Poussin
- http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Quetelet
- For the pictures : word-insert- picture